Development of the tangent linear and adjoint models of the MPAS-Atmosphere dynamic core and applications in adjoint relative sensitivity studies

This study develops and tests a version of the Python-driven, non-hydrostatic Model for Prediction Across Scales – Atmosphere (MPAS-A) dynamic model, as well as its tangent linear and adjoint models. The non-linear, non-hydrostatic dynamic core of the MPAS-A is restructured to have a Python driver for the convenience of parsing namelists, manipulating matrices, controlling simulation time flows, reading model inputs, and writing outputs, while the heavy-duty mediation and model layers are retained in Fortran for computational efficiency. Under the same Python-driving structure, developed are the tangent linear and adjoint models for the dynamic core of the MPAS-A model with verified correctness. The case of Jablonowski and Williamson’s baroclinic wave is used for demonstrating the approximation accuracy of the MPAS-A tangent linear model and the applicability of the MPAS-A adjoint model to relative sensitivity studies. Numerical experimental results show that the tangent linear model can well approximate the temporal evolutions of non-linear model perturbations for all model variables over a four-day forecast period. Employing the MPAS-A adjoint model, it is shown that the most sensitive regions of the 24-h forecast of surface pressure are weather dependent. An interesting westward vertical tilting is also found in the relative sensitivity results of a 24-h forecast of surface pressure at a point located within a trough to model initial conditions. This functionality of the MPAS-A adjoint model is highly essential in understanding dynamics and variational data assimilation.